A spectral condition for odd cycles in non-bipartite graphs

2021 ◽  
Vol 631 ◽  
pp. 83-93
Author(s):  
Huiqiu Lin ◽  
Hangtian Guo
Keyword(s):  
Bipartite Graphs ◽  
Spectral Condition ◽  
Odd Cycles

scholarly journals A spectral condition for odd cycles in graphs

2008 ◽  
Vol 428 (7) ◽  
pp. 1492-1498 ◽  
Author(s):  
Vladimir Nikiforov
Keyword(s):  
Spectral Condition ◽  
Odd Cycles

scholarly journals Biclique edge-choosability in some classes of graphs∗

2017 ◽  
Author(s):  
Gabriel A. G. Sobral ◽  
Marina Groshaus ◽  
André L. P. Guedes
Keyword(s):  
Lower Bound ◽  
Edge Coloring ◽  
Bipartite Graphs ◽  
Polynomial Algorithms ◽  
Odd Cycles ◽  
Chordal Bipartite Graphs

In this paper we study the problem of coloring the edges of a graph for any k-list assignment such that there is no maximal monochromatic biclique, in other words, the k-biclique edge-choosability problem. We prove that the K3free graphs that are not odd cycles are 2-star edge-choosable, chordal bipartite graphs are 2-biclique edge-choosable and we present a lower bound for the biclique choice index of power of cycles and power of paths. We also provide polynomial algorithms to compute a 2-biclique (star) edge-coloring for K3-free and chordal bipartite graphs for any given 2-list assignment to edges.

Gallai–Ramsey Numbers of Odd Cycles and Complete Bipartite Graphs

2018 ◽  
Vol 34 (6) ◽  
pp. 1185-1196 ◽  
Author(s):  
Ming Chen ◽  
Yusheng Li ◽  
Chaoping Pei
Keyword(s):  
Bipartite Graphs ◽  
Ramsey Numbers ◽  
Complete Bipartite Graphs ◽  
Odd Cycles

scholarly journals New proofs of Konig's bipartite graph characterization theorem

2017 ◽  
Vol 1 (2) ◽  
pp. 32
Author(s):  
Salman Fawzi Ghazal
Keyword(s):  
Bipartite Graph ◽  
Spanning Trees ◽  
Characterization Theorem ◽  
Bipartite Graphs ◽  
Odd Cycles

We introduce four new elementary short proofs of the famous K\"{o}nig's theorem which characterizes bipartite graphs by absence of odd cycles. Our proofs are more elementary than earlier proofs because they use neither distances nor walks nor spanning trees.

Edge Maximal Non-Bipartite Graphs Without Odd Cycles of Prescribed Lengths

2002 ◽  
Vol 18 (1) ◽  
pp. 75-92 ◽  
Author(s):  
Louis Caccetta ◽  
Rui-Zhong Jia
Keyword(s):  
Bipartite Graphs ◽  
Odd Cycles

Bipartite Graphs and their Applications

1998 ◽  
Author(s):  
Armen S. Asratian ◽  
Tristan M. J. Denley ◽  
Roland Häggkvist
Keyword(s):  
Bipartite Graphs
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